Preheat oven to 375 degrees F. Cook the sausage, stirring and breaking up into pieces, in a medium skillet over medium-high heat until browned in some spots and cooked through, 6 to 7 minutes. Transfer to a medium bowl and stir in the pizza sauce. Let cool slightly, about 15 minutes.
Coat the back of a baking sheet with cooking spray. Unroll both cans of crescent dough and separate unto 16 triangles. Put a 5-inch ramekin in the center of the prepared baking sheet. Arrange the triangles in a ring around the ramekin so the short sides of the dough are touching the ramekin, overlapping slightly, and the pointed ends are facing outward (it should look like a giant sun).
Spoon the sausage mixture over the short ends of the triangles closest to the ramekin. Cover the sausage with the ham slices. Top the ham with the pepperoni and then cover pepperoni with cheese slices. Remove the ramekin. Take hold of the pointed end of one of the triangles and fold it up and over the filling, tucking the tip under the bottom edge of dough to secure (the dough will not cover the filling completely). Repeat with the remaining triangles (there will be some gaps where you can see the mixture).
Bake until the dough is golden brown and the cheese is melted, about 25 minutes. Brush the dough with the butter and sprinkle with the Italian seasoning. Let cool for 15 minutes. Use a spatula to slide the ring off the baking sheet onto a platter. Serve with more pizza sauce.
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